# Derived rule

of a derivation in a given calculus

A derivation rule whose conclusion is derivable from its premises in the calculus under consideration. For example, in propositional calculus the derivation rule

$$\frac{A\supset B,B\supset C}{A\supset C}$$

is a derived rule, since in this calculus there is derivability from the premises:

$$A\supset B,B\supset C\vdash A\supset C.$$

Every derived rule is a sound rule, but not every sound rule is a derived rule. For example, the substitution rule in propositional calculus is a sound but not a derived rule.

#### References

 [1] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1951)
How to Cite This Entry:
Derived rule. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Derived_rule&oldid=33735
This article was adapted from an original article by S.N. Artemov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article